Setting the texture's grayscale as alpha?
Here is the way I would do what I think you're asking. I plugged to color data into a Color Ramp and plugged that into the Alpha channel. There is also a SeparateHSV node that might work well between the Color output and the Color Ramp. For Eevee, you need to go into Settings and set the Blend Mode. In the picture it is set to Alpha Blend.

Another way of doing it is to mix an emission shader and a transparent shader, assuming this is meant as a light. For this screen shot I added another white cube behind the blue object and turned on Eevee's 'bloom'